Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method
A hybrid higher-order finite element boundary integral (FE-BI) technique is discussed where the higher-order FE matrix elements are computed by a fully analytical procedure and where the gobal matrix assembly is organized by a self-identifying procedure of the local to global transformation. This as...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | deu |
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Copernicus Publications
2014-11-01
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| Series: | Advances in Radio Science |
| Online Access: | http://www.adv-radio-sci.net/12/1/2014/ars-12-1-2014.pdf |
| _version_ | 1818563103455969280 |
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| author | L. Li K. Wang H. Li T. F. Eibert |
| author_facet | L. Li K. Wang H. Li T. F. Eibert |
| author_sort | L. Li |
| collection | DOAJ |
| description | A hybrid higher-order finite element boundary integral (FE-BI) technique is
discussed where the higher-order FE matrix elements are computed by a fully
analytical procedure and where the gobal matrix assembly is organized by a
self-identifying procedure of the local to global transformation. This
assembly procedure applys to both, the FE part as well as the BI part of the
algorithm. The geometry is meshed into three-dimensional tetrahedra as finite
elements and nearly orthogonal hierarchical basis functions are employed. The
boundary conditions are implemented in a strong sense such that the boundary
values of the volume basis functions are directly utilized within the BI,
either for the tangential electric and magnetic fields or for the asssociated
equivalent surface current densities by applying a cross product with the
unit surface normals. The self-identified method for the global matrix
assembly automatically discerns the global order of the basis functions for
generating the matrix elements. Higher order basis functions do need more
unknowns for each single FE, however, fewer FEs are needed to achieve the
same satisfiable accuracy. This improvement provides a lot more flexibility
for meshing and allows the mesh size to raise up to λ/3. The
performance of the implemented system is evaluated in terms of computation
time, accuracy and memory occupation, where excellent results with respect to
precision and computation times of large scale simulations are found. |
| first_indexed | 2024-12-14T01:12:27Z |
| format | Article |
| id | doaj.art-ebec922d51a84a11ac1ba632a8c16496 |
| institution | Directory Open Access Journal |
| issn | 1684-9965 1684-9973 |
| language | deu |
| last_indexed | 2024-12-14T01:12:27Z |
| publishDate | 2014-11-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Advances in Radio Science |
| spelling | doaj.art-ebec922d51a84a11ac1ba632a8c164962022-12-21T23:22:41ZdeuCopernicus PublicationsAdvances in Radio Science1684-99651684-99732014-11-011211110.5194/ars-12-1-2014Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral methodL. Li0K. Wang1H. Li2T. F. Eibert3Technische Universität München, Lehrstuhl für Hochfrequenztechnik, Arcisstrasse 21, 80333 Munich, GermanyTechnische Universität München, Lehrstuhl für Hochfrequenztechnik, Arcisstrasse 21, 80333 Munich, GermanyPolitecnico di Torino, Electronic and Telecommunication, Corso Duca degli Abruzzi, 24, 10129 Torino, ItalyTechnische Universität München, Lehrstuhl für Hochfrequenztechnik, Arcisstrasse 21, 80333 Munich, GermanyA hybrid higher-order finite element boundary integral (FE-BI) technique is discussed where the higher-order FE matrix elements are computed by a fully analytical procedure and where the gobal matrix assembly is organized by a self-identifying procedure of the local to global transformation. This assembly procedure applys to both, the FE part as well as the BI part of the algorithm. The geometry is meshed into three-dimensional tetrahedra as finite elements and nearly orthogonal hierarchical basis functions are employed. The boundary conditions are implemented in a strong sense such that the boundary values of the volume basis functions are directly utilized within the BI, either for the tangential electric and magnetic fields or for the asssociated equivalent surface current densities by applying a cross product with the unit surface normals. The self-identified method for the global matrix assembly automatically discerns the global order of the basis functions for generating the matrix elements. Higher order basis functions do need more unknowns for each single FE, however, fewer FEs are needed to achieve the same satisfiable accuracy. This improvement provides a lot more flexibility for meshing and allows the mesh size to raise up to λ/3. The performance of the implemented system is evaluated in terms of computation time, accuracy and memory occupation, where excellent results with respect to precision and computation times of large scale simulations are found.http://www.adv-radio-sci.net/12/1/2014/ars-12-1-2014.pdf |
| spellingShingle | L. Li K. Wang H. Li T. F. Eibert Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method Advances in Radio Science |
| title | Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method |
| title_full | Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method |
| title_fullStr | Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method |
| title_full_unstemmed | Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method |
| title_short | Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method |
| title_sort | analytical finite element matrix elements and global matrix assembly for hierarchical 3 d vector basis functions within the hybrid finite element boundary integral method |
| url | http://www.adv-radio-sci.net/12/1/2014/ars-12-1-2014.pdf |
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